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Let's review the steps involved in simplifying square roots:
To simplify the square root of a fraction, simplify the numerator and simplify the denominator.
Example 1: Simplify
In addition to simplifying the numerator and the denominator in a fraction, it is mathematical convention to rationalize the denominator--that is, to write the fraction as an equivalent expression with no roots in the denominator.
To rationalize a denominator, multiply the fraction by a "clever" form
of 1--that is, by a fraction whose numerator and denominator are
both equal to the square root in the denominator. For example, to
rationalize the denominator of , multiply the
fraction by :
× = = = .
Thus, = .
Often, the fraction can be reduced:
Rationalize the denominator of :
× = = = = 3.
Thus, = 3.
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